Samantha opened a savings account and deposited $8192. The account earns 10% in interest annually. She makes no further deposits and does not withdraw any money. In t years, she has $25,710 in this account. Write an equation in terms of t that models the situation.
The equation in terms of t that models the situation is given by
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex].
We know that the interest on a loan or deposit that is accrued on both the initial principal and the total interest from prior periods is known as compound interest and it can be calculated as
[tex]A = P(1+\frac{r}{n})^{nt}[/tex],
where P is the initial principal, r is the rate of interest, n is the number of times interest was charged for each time period, t is the amount of time that has passed and A is the final amount.
Here, P = 8192, r = 10% = 10/100 = 0.01, n = 12 and A = 25,710
So, we can write
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex]
Therefore the required equation is
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex]
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QUESTION 8 - 1 POINT
The median monthly rent in 1994 was $499 and $633 in 2001. What was the percent increase in the
median monthly rent prices from 1994 to 2001? Round to the nearest tenth of a percent.
Answer:
26.85%
Step-by-step explanation:
first you find the difference in price increase
633-499=134
*percentage increase=increase value/original value x100
so;=134/499x100=28.85%
hope it helps you.please don't forget to give me a thanks
solve for x: 5x-4y=24
Answer:
x=4y+24/5
Step-by-step explanation:
add 4y
Divide by 5
NEED HELP ASAP WILL MARK BRAINLIEST!
Answer:
log_{b} (5b) = 2.609
Given that:
log_{b} (3) = 1.099
log_{b} (5) = 1.609
Evaluating with that:
[tex]\sf log_b (5b) = log_b\left(5\right)+log_b\left(b\right)[/tex]
[tex]= \sf 1.609 + 1[/tex]
[tex]= \sf 2.609[/tex]
Rule Used:
[tex]\rm \log _a\left(xy\right)=\log _a\left(x\right)+\log _a\left(y\right)[/tex]
evaluate this exponential expression 5 • (3 + 6)^2 - 6^2
The answer of this expression is 369
We know that to solve a numerical expression, we will calculate with property base form.
When there are symbols in an expression, we first solve the numbers in order that are between:
Parentheses ( ) Brackets [ ] Braces { }The math signs calculated first in order are;
Power - square root Multiplication - divisionAddition - subtractionGiven the expression, the resolution will be:
5 * ( 3 + 6 )² - 6²
5 * 9² - 6²
5 * 81 - 36
406 - 36
369
So, the value of this numeric expression is 369
Find the domain and range
Answer:
Domain: (-∞, ∞)
Range: [-2, ∞)
Step-by-step explanation:
The domain of any parabola is (-∞, ∞)
The range of this parabola is [-2, ∞) because the vertex is at (-2, -2).
From this diagram, select the
pair of lines that must be
parallel if angle 1 is congruent to angle 8. If there is no pair of lines, select "none".
Answer:
Line L is parallel to Nangle 1 is equal to angle 4 ( vertically opposite angles)
if angle 1 is congruent to angle 8
then angle 4 is also congruent to angle 8
then slope of line L and n is equal
that is L is parallel to n
Which choices are equivalent to the expression below? Check all that apply. √8 × √8
A. √ 8
B. 8
C. 64
D. 8
E. 16
F. √64
Answer:
the answers are B and F since √8 x √8 = √64 which simplifies to 8.
How much would it cost to buy a piece of candy for 50 cents plus tax
Answer:
it depends on which state your in or in your even in the us usually it is either 6% or 4% some times more or less % so im going to do both
50*0.06=53
50*0.04=52
Hope This Helps!!!
What is the value of the expression 24 + 3²? What is the value of the expression 24 + 3² ?
Answer:
33
Step-by-step explanation:
3² = 3.3 = 9 => 24 + 9 = 33
By selling a table for sh.56, gain is as much as percent as its cost in dollars. What is the cost price? By selling a table for sh.56 , gain is as much as percent as its cost in dollars . What is the cost price ?
The cost price of the table is $40.
What is Gain ?Gain is the amount gain by selling the product at a higher price than its cost.
Let the cost of the table is $ x
The percentage gain is x% (as given in the question)
Cost price = ?
It is known that
Step 1 : Gain = ( selling Price - Cost Price) * 100 / Cost Price
Selling price = 56
Cost Price = $ x
Therefore substituting the value
x = (56 - x) * 100 / x
x² = 5600 - 100x
x² +100x -5600 = 0
Step 2 : Factorizing
x² + 140x - 40 x -5600 = 0
x( x+14 ) -40( x +14) = 0
( x - 40)(x +14) = 0
x = $40
Therefore the cost price of the table is $40.
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Which of the numbers below are whole numbers? Check all that apply.
A. 6830
B. 66
C. 717.59
D. 808
E. 42.3
F. 1/10
Step-by-step explanation:
Anything which has a decimal point is not a whole number
6830 is
66 is
717.59 is not
808 is
42.3 is not
1/10 = 0.1 ergo is not
Which expression is equivalent to...
Answer:
A is correct yes
Step-by-step explanation:
ndnanndnqnjed
Consider figures 1 and 2 shown in the coordinate plane. Figure 1 has been transformed to produce figure 2.
Answer:
0 and -6
(0,-6)
Step-by-step explanation:
Can't really explain, but this is a guess on the actual question.
ING DROPS
1. The total volume to be given is 30 ml.
The time over which this is to be given is 30 minutes.
The drop factor is 15.
How many drops per minute will be delivered ?
Answer:
15 drops per minute
Step-by-step explanation:
(drops per minute) flow/drip rate: volume ÷ time × drop factor
note:
volume (mL)
time (minutes)\
30 / 30 = 1
1 * 15 = 15
so, 15 drops per minute will be delivered
hope this helps!! have a lovely day :)
Answer:
15 drops/minute
Step-by-step explanation:
30 ÷ 30 = 1
1 · 15 = 15
hope this is helpful :)
A researcher conducts an between-subjects study examining the
effectiveness of a memory enhancement program at an assisted living
facility for elderly adults. One group of residents is selected to
participate in the program, and a second group of participants serves as
a control group. After 6 weeks, the researcher reports a combined score
measuring memory for each individual. The data are:
Control
Exercise
n = 10
M = 12
SS = 120.5
n=15
M= 15.5
SS = 190.0
a) Does the exercise program have a significant effect? Use a two
tailed test with an alpha level of .05
b) Compute Cohen's d to measure the size of the treatment effect
H0: µ1 = µ2; The exercise program do not have significant effect on physical fitness, H1: µ1 =/ µ2; the exercise program had a significant effect on physical fitness and the Estimated Cohen's d is 0.82.
HypothesisA. Significant effect
H0: µ1 = µ2
Based on the above hypothesis the exercise program does not have significant effect on physical fitness
H1: µ1 =/ µ2
Based on the above hypothesis the exercise program had a significant effect on physical fitness
Pooled variance: sp2 = (190 + 120.5/(15-1) + (10-1)
Pooled variance: sp2 = 310.5/23
Pooled variance: sp2 =13.5
Estimated standard error ( sM1-M2):
sM1-M2 =√13.5/15 +13.5/10
sM1-M2 =√2.25
sM1-M2 = 1.5
Tailed test (t)
t = (15.5 - 12)/1.5
t=3.5/1.5
t= 2.33
B. Estimated Cohen's d:
Estimated Cohen's d = 3/√13.5
Estimated Cohen's d = 3/3.67
Estimated Cohen's d= 0.817
Estimated Cohen's d= 0.82 (Approximately); this is a large effect.
Conclusion demonstrating how the outcome of the hypothesis test would tend to appear in a research report is: (Reject H0). Because the group exercise program tend to have a significant effect on the physical fitness of elderly adults, t = 2.33, p <.05, d = 0.82.
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a plane intersects a sphere 5 cm away from the center of the sphere. the cross section is a circle whose diameter is 12cm. determine the radius of the sphere
Answer:
7.81 cm
Step-by-step explanation:
diameter = 12, 12/2 = 6
(r+5)(r-5) = 6 * 6
r^2 - 25 = 36
r^2 = 61
r = 7.81
radius = 7.81 cm
Answer:
26
Step-by-step explanation:
What negative Z-score (standard score) would the area under the curve be 0.8621
z* = _______
Find the y-intercept.
(2x + 1)(x + 7).
(x + 3)(x + 4)
y =
([?],
all three would be pretty nice
Answer:
(0, 7/12)
Step-by-step explanation:
to find the y intercept we equate x to 0.
hence,
f(0) = 7/12
the coordinate is (0, 7/12)
Answer:
[tex](0,\frac{7}{12})[/tex]
Step-by-step explanation:
In order to find the y-intercept of an equation, simply plug in 0 for x, as that's where the y-axis is.
[tex]\frac{(2(0)+1)(0+7)}{((0)+3)((0)+4)}[/tex]
Simplify:
[tex]\frac{7}{(3)(4)}=\frac{7}{14}[/tex]
Therefore, the y-intercept for the equation is:
[tex]\frac{7}{14}[/tex]
Translate the phrase; then simplify. Find the sum of −45, −13, and 37.
Answer:
-21
Step-by-step explanation:
37 - 45 - 13 is translated
-8 - 13
-21
Help I have no idea to do this!! I’m stuck!
Answer: 7
Step-by-step explanation:
[tex]A \cap C[/tex] denotes the intersection of A and C, or in other words, how many elements are shared between them.
The number of elements is 2 + 5 = 7
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: a = -1[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
For a function f(x) = y,
x represents the value ( x - coordinate ) at which the function has a value y.
[tex]\qquad \tt \rightarrow \: f(x) = a {x}^{2} + 2[/tex]
for point (-1 , 1) to satisfy the equation, we have to calculate the value of a
[tex]\qquad \tt \rightarrow \: f( - 1) = a( - 1) {}^{2} + 2[/tex]
[tex]\qquad \tt \rightarrow \: 1 = a + 2[/tex]
[tex]\qquad \tt \rightarrow \: a = 1 - 2[/tex]
[tex]\qquad \tt \rightarrow \: a = - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Substitute -1 into x
Substitute 1 into y
f(x)= a (-1) ^2+2=1
a=-1
Find f ° g and g ° f, if they exist. f={(-4,-5),(0,3),(1,6)} and g={(-5,0),(3,-4),(6,1)}.
The composite function of f o g are (-4,-5),(0,3),(1,6). The composite function of g o f are (-5,0),(3,-4),(6,1).
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
Given;
f = {(-4,-5),(0,3),(1,6)}
g = {(-5,0),(3,-4),(6,1)}.
In order to find f o g and g o f,
f o g = f(g)
The composite function of f o g
f(-5,0) = (-4,-5)
f(3,-4) = (0,3)
f(6,1) = (1,6)
The composite function of g o f
g(-4,-5) = (-5,0)
g(0,3) = (3,-4)
g (1,6) = (6,1)
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The solution set to 6 + 2n > 12 is n > 3. Which are correct representations of this solution? Select two options.
{n | n < 3}
{n | n ≥ 3}
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to positive 5.
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to negative 5.
(3, ∞)
The correct representations of this solution are
(d) A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to negative 5.(e) (3, ∞)How to determine the solution set?The inequality is given as:
6 + 2n > 12
The solution is given as:
n > 3
When the above inequality is represented as an interval, we have:
(3, ∞)
Also, the inequality symbol > is represented using an open circle.
This means that the number line would use an open circle and the arrow would point right
Hence, the correct representations of this solution are (d) and (e)
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Migdalia is a consultant. She works 3 days a week in the company's headquarters and 2
week at a production site.When she works at the company headquarters, she takes a bus
from work. When she goes to production sites, she uses her car and travels 52 ms
cast for using the bus is $48.00 for 10 one-way trips. The cost of using her car she
30 per mile Migdalia budgets $50 per week for travel expenses to and from work whether or not she has set aside enough money.
Since she has set aside only $50 for the trip, she hasn't set aside enough money for the trip
How to find the expenses and know if it's enough?She works 3 days in a week in the headquarter and 2 days a week at the production site.
When she works at the company headquarters, she takes a bus to and from work. The cost for using the bus is $48.00 for 10 one-way trips.
Therefore,
each one way trip = 48 / 10 = $4.8
To and from the headquarters = 4.8 × 2 = $9.6
Hence,
Therefore,
three days cost = 9.6 × 3 = $28.8
The cost of using her car she estimates at 30 cent per mile. When she goes to production sites, she uses her car and travels 52 miles per day. Therefore,
cost of travelling to production site in a week = 2 × (52 × 0.3) = $31.2
Hence,
cost of expenses per week = 31.2 + 28.8 = $60
Since she has set aside only $50 for the trip, she hasn't set aside enough money for the trip
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Basically look at the picture I don’t even know what to say
Answer:
C
Step-by-step explanation:
x = [tex]\frac{2}{3}[/tex] πr³ ( multiply both sides by 3 to clear the fraction )
3x = 2πr³ ( divide both sides by 2π )
[tex]\frac{3x}{2\pi }[/tex] = r³ ( take cube root of both sides )
[tex]\sqrt[3]{\frac{3x}{2\pi } }[/tex] = r
Answer:
[tex]r=\sqrt[3]{\frac{3x}{2\pi }}[/tex]
Step-by-step explanation:
This question make look scary, but don't judge its book by its cover.
[tex]x=\frac{2}{3} \pi r^{3} \\\frac{2}{3} \pi r^{3}=x\\r^{3} =x / \frac{2\pi }{3} \\r^{3} =x*\frac{3}{2\pi } \\r^{3} =\frac{3x}{2\pi } \\r=\sqrt[3]{\frac{3x}{2\pi }}[/tex]
A line / passes through point (-2, 5) and has the same y-intercept as
the line y-3x-4. What is the equation for the line /?
I'm assuming you meant to write y = 3x-4
We know that the y-intercept of the given line is (0,-4), so we need to find the equation of the line passing through (-2,5) and (0,-4).
The slope is
[tex]\frac{-4-5}{0-(-2)}=-\frac{9}{2}[/tex]
So, this means the equation is [tex]\boxed{y=-\frac{9}{2}x-4}[/tex]
Find the solutions to the equation below. check all that apply. x^2-2x-15=0
The student did not make any mistake, the solution is correct. Then the correct option is A.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
A student perform the following steps to find the solution of the equation x² – 2x – 15 = 0.
The factor of the equation will be
Step 1 : x² – 2x – 15 = (x – 5)(x + 3)
Step 2 : (x – 5) = 0 and (x + 3) = 0
Step 3 : x = 5 and – 3
The student did not make any mistake, the solution is correct.
Then the correct option is A.
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Find the numeral preceding and succeeding each of the following numerals. Use T as the digit for 10.
a. TTO eleven
b. 100000 nine
c. 222 three
The numeral preceding and succeeding each of the following numerals.
Now, what happens when you add 1 or subtract 1 from 100 in the familiar base 10.
Adding adds 1 to the unit digit.
Subtracting 1 gives 99 because 9 is the largest digit in base 10.
So A. 100 base 8
The largest digit in base 8 is 7, so
..., 77, 100, 101,...
B. 10000 base 7
What is the largest digit in base 7?
The largest digit in base 7 is 6, so
..., 6666, 10000, 10001, ...
Next what happens when you add 1 to 509 in base 10. 9 is the largest digit in base 9, so adding 1 makes the units digit 0, and you carry a 1 to the next digit to the left:
509 + 1 = 510.
C. 305 base 6
5 is the largest digit in base 6, so
..., 304, 305, 310, ...
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determined about the triangle formed by the ground,
wall, and ladder? Check all that apply.
The triangle is isosceles.
The leg-to-hypotenuse
ratio is 1:√√2.
The leg-to-hypotenuse ratio is 1:√2.
The nonright angles are congruent.
The ladder represents the longest length in the
triangle.
(A,B,D,E)
Answer:
a² b² c² equals mc² and that is the answer
